北航数学论坛学术报告

Communication-Efficient Distributed Linear Discriminant Analysis for Binary Classification

赵俊龙教授

（北京师范大学）

报告时间：10：00-11：30，2021-6-22（星期二）

报告地点： 腾讯会议ID:740407877

报告摘要： Large-scale data are common when the sample size n is large, and these data are often stored on k different local machines. Distributed statistical learning is an efficient way to deal with such data. In this study, we consider the binary classification problem for massive data based on a linear discriminant analysis (LDA) in a distributed learning framework. The classical centralized LDA requires the transmission of some p-by-p summary matrices to the hub, where p is the dimension of the variates under consideration. This can be a burden when p is large or the communication costs between the nodes are expensive. We consider two distributed LDA estimators, two-round and one-shot estimators, which are communication-efficient without transmitting p-by-p matrices. We study the asymptotic relative efficiency of distributed LDA estimators compared to a centralized LDA using random matrix theory under different settings of k. It is shown that when k is in a suitable range, such as k = o(n/p),these two distributed estimators achieve the same efficiency as that of the centralized estimator under mild conditions. Moreover, the two-round estimator can relax the restriction on k, allowing kp/n ->c 2 [0, 1) under some conditions. Simulations confirm the theoretical results.

报告人简介：赵俊龙， 北京师范大学统计学院教授

研究领域：高维数据分析、稳健统计，统计机器学习。在统计学各类期刊发表SCI论文四十余篇，部分结果发表在统计学顶级期刊Journal of the Royal Statistical Society: Series B（JRSSB）、The Annals of Statistics（AOS）、Journal of American Statistical Association(JASA)，Biometrika等。

邀请人： 陈迪荣